For the following questions answer them individually
The ten digit number 2x600000y8 is exactly divisible by 24. If x ≠0 and y ≠0, then the least value of (x + y) is equal to:
O, G, and H arerespectively the circumcentre, centroid, incentre and orthocentre of an equilateral triangle. Which of these points are identical ?
A certain sum was invested on simple interest. The amount to which it had grown in five years was $$1\frac{1}{4}$$ times the amount to which it had grown in three years. The percentage rate of interest was:
A can complete a piece of work in 20 days and B can complete 20% of the work in 6 days. If they work together in how many dayscan they finish 50% of the work, if they work together ?
What is the value of $$\cosec^2 30^\circ + \sin^2 45^\circ + \sec^2 60^\circ + \tan^2 30^\circ$$ ?
$$\triangle ABC \sim \triangle DEF$$ and their perimeters are 64 cm and 48 cm respectively. What is the length AB, if DE is equal to 9 cm ?
If $$(3x + 1)^3 + (x - 3)^3 + (4 - 2x)^3 + 6 (3x + 1)(x - 3)(x - 2) = 0$$, then $$x$$ is equal to:
For $$0^\circ \leq \theta \leq 90^\circ$$, what is $$\theta$$, when $$\sqrt3 \cos \theta + \sin \theta = 1$$ ?
During a practice session in a stadium an athlete runs along a circular track and her performance is observed by her coach standing at a point on the circle and also by her physiotherapist standing at the centre of the circle. The coach finds that she covers an angle of $$72^\circ$$ in 1 min. What will be the angle covered by her in 1 second according to the measurement made by her physiotherapist ?
